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BEGIN:VEVENT
SUMMARY:Bojko Bakalov (North Carolina State University)
DTSTART:20200908T170000Z
DTEND:20200908T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/1
DESCRIPTION:Title: A vertex algebra construction of representations of toroi
dal Lie algebras\nby Bojko Bakalov (North Carolina State University) a
s part of Representation Theory and Mathematical Physics Seminar\n\n\nAbst
ract\nGiven a simple finite-dimensional Lie algebra and an automorphism of
\nfinite order\, one can construct a twisted toroidal Lie algebra.\nSimila
rly to twisted affine Lie algebras\, which are well-studied in\nthe litera
ture\, we can create representations of twisted toroidal Lie\nalgebras wit
h the help of vertex algebras. In this talk\, I will\ndiscuss twisted modu
les of vertex algebras and will show how\nrepresentations of twisted toroi
dal Lie algebras can be constructed\nfrom such twisted modules. Joint work
with Samantha Kirk.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Feigin (University of Glasgow)
DTSTART:20200915T170000Z
DTEND:20200915T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/2
DESCRIPTION:Title: Lassalle-Nekrasov correspondence for Calogero-Moser syste
ms and quasi-invariant Hermite polynomials\nby Misha Feigin (Universit
y of Glasgow) as part of Representation Theory and Mathematical Physics Se
minar\n\n\nAbstract\nLassalle and Nekrasov observed in the 1990s relations
between the rational Calogero-Moser system with harmonic term and the tri
gonometric Calogero-Moser system. In the quantum case this amounts to an o
perator on the algebra of symmetric polynomials which intertwines actions
of corresponding quantum integrals of these two systems. I would like to e
xplain this relation and its generalisations by making use of automorphism
s of the rational Cherednik algebra. For integer coupling parameter the al
gebra of symmetric polynomials can be extended by quasi-invariants\, which
is a module for the spherical subalgebra of Cherednik algebra\, and we ge
t a class of non-symmetric polynomials which are eigenfunctions of the rat
ional Hamiltonian. The talk is based on joint work with Martin Hallnäs an
d Alexander Veselov.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saber Ahmed (University of Texas at Arlington)
DTSTART:20200922T170000Z
DTEND:20200922T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/3
DESCRIPTION:Title: Quantized enveloping superalgebra of type $P$\nby Sab
er Ahmed (University of Texas at Arlington) as part of Representation Theo
ry and Mathematical Physics Seminar\n\n\nAbstract\nWe introduce a new quan
tized enveloping superalgebra $U_q({\\mathfrak p}(n))$ that is a quantizat
ion of the Lie bisuperalgebra structure on the periplectic Lie superalgebr
a ${\\mathfrak p}(n)$. We show some of the basic properties of the quantiz
ation. We also introduce the periplectic $q$-Brauer algebra. This is a joi
nt work with D. Grantcharov and N. Guay.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddhartha Sahi (Rutgers University)
DTSTART:20200929T170000Z
DTEND:20200929T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/4
DESCRIPTION:Title: Lie superalgebras and the Capelli eigenvalue problem\
nby Siddhartha Sahi (Rutgers University) as part of Representation Theory
and Mathematical Physics Seminar\n\n\nAbstract\nThe classical Capelli oper
ator of 19th century invariant theory is a differential operator on $n \\t
imes n$ matrices\, which is closely related to the determinant. In the 198
0s\, Bertram Kostant and the speaker found a natural generalization of thi
s to a Jordan algebra $J$\, with the determinant replaced by the Jordan no
rm polynomial.The differential operators that arise in this manner belong
to the algebra $D(X)$ of invariant differential operators on a certain sym
metric space $X$ associated to $J$.\n\n In the 1990s\, the speaker exte
nded these ideas to obtain a *basis* of $D(X)$\, now called the "Capelli b
asis"\, and computed their eigenvalues. By a general result of Harish-Chan
dra\, the eigenvalues of an invariant differential operator $T$ are specia
l values of an associated Weyl group invariant polynomial $p_T$. For the C
apelli basis\, the polynomials $p_T$ are special cases of a remarkable fam
ily of polynomials defined by certain elementary vanishing conditions\, or
interpolation properties.\n\n Subsequently\, Friedrich Knop and the spe
aker discovered an unexpected connection between the more general "interpo
lation polynomials" and Jack polynomials. This led to new insights into Ja
ck polynomials\, and subsequently for Macdonald polynomials and double aff
ine Hecke algebras\, resulting in the proofs of certain conjectures by Mac
donald.\n\n In this talk I will describe the extension of some of these
ideas to Jordan superalgebras and symmetric superspaces obtained in recen
t work by Vera Serganova\, Hadi Salmasian\, and the speaker\, building on
earlier joint work with Salmasian and Alexander Alldridge. This offers som
e new insights into the representation theory of Lie superalgebras. It als
o opens a new perspective on interpolation polynomials themselves\, reveal
ing a connection with Deligne's interpolation categories. It has also reve
aled a remarkable new connection with something almost as old as the origi
nal Capelli operator\, namely the Dougall-Ramanujan identity\, dubbed by E
khad and Zeilberger as "one of the most beautiful and general results in t
he theory of hypergeometric series".\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Futorny (Universidade de Sao Paulo)
DTSTART:20201006T170000Z
DTEND:20201006T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/5
DESCRIPTION:Title: Positive energy representations of affine vertex algebras
via localization\nby Vyacheslav Futorny (Universidade de Sao Paulo) a
s part of Representation Theory and Mathematical Physics Seminar\n\n\nAbst
ract\nThis is a joint work with Libor Krizka. We introduce a Wakimoto func
tor from a certain category of modules over a simple finite-dimensional Li
e algebra to the category of positive energy modules over the correspondin
g affine Kac-Moody algebra. Combining the Wakimoto functor with the local
ization functor we construct new families of positive energy representatio
ns of affine vertex algebras together with their free field realizations.
\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Morier-Genoud (Sorbonne Université\, Paris)
DTSTART:20201013T170000Z
DTEND:20201013T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/6
DESCRIPTION:Title: $q$-analogues of rational and real numbers\nby Sophie
Morier-Genoud (Sorbonne Université\, Paris) as part of Representation Th
eory and Mathematical Physics Seminar\n\n\nAbstract\nClassical sequences o
f numbers often lead to interesting $q$-analogues. The most popular among
them are certainly the $q$-integers and the $q$-binomial coefficients whic
h both appear in various areas of mathematics and physics. It seems that q
-analogues of rational numbers have been much less popular so far. We sugg
est a definition based on combinatorial properties of the rational numbers
and continued fractions. The definition of $q$-rationals naturally extend
s the one of $q$-integers and leads to a ratio of polynomials with positiv
e integer coefficients. One can give enumerative interpretations of the co
efficients in terms of graphs or quiver representations. There are also li
nks to the Jones polynomials and to cluster algebras. Finally the definiti
on of q-rationals extends to a definition for $q$-real numbers. This is jo
int work with Valentin Ovsienko.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vera Serganova (University of California\, Berkeley)
DTSTART:20201020T170000Z
DTEND:20201020T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/7
DESCRIPTION:Title: Tensor product of the Fock representation with its dual.<
/a>\nby Vera Serganova (University of California\, Berkeley) as part of R
epresentation Theory and Mathematical Physics Seminar\n\n\nAbstract\nLet $
F$ denote the Fock representation for $sl(\\infty)$. We describe the struc
ture of the tensor product of $F$ with its restricted dual $F^*$. In parti
cular we prove that this module has a decreasing filtration with simple qu
otients and show that such filtration is unique. The proof uses categorifi
cation of the abelian envelope of Deligne category $GL(t)$ for integer $t$
and the category of finite-dimensional representations of the supergroup
$GL(m|n)$ with $m-n=t$.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik (Weizmann Institute of Science)
DTSTART:20201027T170000Z
DTEND:20201027T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/8
DESCRIPTION:Title: Arc diagrams and Duflo-Serganova functor $DS_x$\nby M
aria Gorelik (Weizmann Institute of Science) as part of Representation The
ory and Mathematical Physics Seminar\n\n\nAbstract\nLet $L$ be a simple f
inite-dimensional module over a Lie superalgebra $\\mathfrak g$. We would
like to describe the $DS_x({\\mathfrak g})$-module $DS_x(L)$. For the al
gebras $\\mathfrak{gl}(m|n)$\, $\\mathfrak{osp}(m|n)$ and $\\mathfrak{p}(n
)$\, the answer can be nicely expressed in terms of a combinatorial gadget
\, the arc diagram\, assigned to $L$. In this talk I will review the cons
tructions of arc diagrams. The talk is based on the results of Heidersdorf
- Weissauer\, Entova-Aizenbud - Serganova and Gorelik - Heidersdorf.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan van de Leur (Utrecht University)
DTSTART:20201103T180000Z
DTEND:20201103T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/9
DESCRIPTION:Title: The Extended Toda and Non-Linear Schroedinger Hierarchies
\nby Johan van de Leur (Utrecht University) as part of Representation
Theory and Mathematical Physics Seminar\n\n\nAbstract\nWe study the integr
able system which is related a Dubrovin–Frobenius manifold of rank $2$ w
hose genus expansion $D$ at a special point controls enumeration of a high
er genera generalization of the Catalan numbers. In particular\, we will g
ive a Hirota bilinear equation for this $D$ and show that this leads to a
Lax formulation of both the Carlet-Dubrovin-Zhang Extended Toda Hierarch a
nd to the extended Non-Linear Schroedinger hierarchy. This is based on joi
nt work with Guido Carlet\, Hessel Posthuma and Sergey Shadrin.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Letterio Gatto (Politecnico di Torino)
DTSTART:20201110T180000Z
DTEND:20201110T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/10
DESCRIPTION:Title: Bosonic and Fermionic Representations of Endomorphisms o
f Exterior Algebras\nby Letterio Gatto (Politecnico di Torino) as part
of Representation Theory and Mathematical Physics Seminar\n\n\nAbstract\n
The abstract is available at:\nhttps://www.math.ksu.edu/research/files_mat
hphysrep_seminar/KSU_RTMPS_Gatto.pdf\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Mnev (University of Notre Dame)
DTSTART:20201117T180000Z
DTEND:20201117T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/11
DESCRIPTION:Title: Two-dimensional BF theory as a conformal field theory\nby Pavel Mnev (University of Notre Dame) as part of Representation Theo
ry and Mathematical Physics Seminar\n\n\nAbstract\nWe study topological BF
theory on the complex plane in Lorenz gauge. In the abelian case\, we fin
d that the gauge-fixed theory is a B-twisted $N=(2\,2)$ superconformal the
ory - Witten's B-model with a parity-reversed target. The BV algebra struc
ture on 0-observables is constructed explicitly using operator product exp
ansions with the superpartner of the stress-energy tensor. In the non-abe
lian case\, the theory becomes a logarithmic CFT with correlators given by
convergent integrals (e.g.\, 4-point functions are expressed in terms of
dilogarithms). We find vertex operators in the non-abelian theory\, receiv
ing a quantum correction to conformal dimension. This is a report on a joi
nt work with Andrey Losev and Donald Youmans\, arXiv:1712.01186\, arXiv:19
02.02738\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (University of Virginia)
DTSTART:20201201T180000Z
DTEND:20201201T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/12
DESCRIPTION:Title: Symmetric functions from integrable vertex models\nb
y Leonid Petrov (University of Virginia) as part of Representation Theory
and Mathematical Physics Seminar\n\n\nAbstract\nI will discuss how propert
ies of symmetric functions (such as Schur and Hall-Littlewood functions an
d their generalizations) arise from studying integrable vertex models. The
focus will be on (1) summation identities\; (2) a new class of continuous
ly-indexed spin Whittaker symmetric functions generalizing the 2F1 hyperge
ometric functions and the gl_n Whittaker functions. The second part is bas
ed on a joint work with Matteo Mucciconi.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Hartwig (Iowa State University)
DTSTART:20210126T180000Z
DTEND:20210126T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/13
DESCRIPTION:Title: Harish-Chandra modules over orders in smash products
\nby Jonas Hartwig (Iowa State University) as part of Representation Theor
y and Mathematical Physics Seminar\n\n\nAbstract\nFor an integral domain $
\\Lambda$ with fraction field $L$\, we study a class of noncommutative $\\
Lambda$-orders $F$ in a smash product of $L$ by a Hopf algebra. Specifical
ly we give a sufficient condition for there to be only finitely many isocl
asses of simple $F$-modules that are locally finite for $\\Lambda$ and are
supported on a given maximal ideal of $\\Lambda$. This generalizes a "fin
iteness of fibers" theorem of Futorny and Ovsienko for Galois orders. We p
oint out some connections to Gelfand-Tsetlin theory for $\\mathfrak{gl}_n$
\, Hopf Galois extensions and Cherednik algebras.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mazorchuk (Uppsala University)
DTSTART:20210202T180000Z
DTEND:20210202T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/14
DESCRIPTION:Title: Images of simple modules under projective functors and K
ostant's problem\nby Volodymyr Mazorchuk (Uppsala University) as part
of Representation Theory and Mathematical Physics Seminar\n\n\nAbstract\nI
n this talk I will try to report on recent progress in connection to the c
lassical Kostant's problem which asks when the unviersal enveloping algebr
a surjects onto the space of adjointly finite endomorphisms of a simple hi
ghest weight module. In particular\, I will describe how this is connect t
o the problem of indecomposability of images of simple highest weight modu
les under indecomposable projective\nfunctors.\n This is a joint work with
Hankyung Ko and Rafael Mrden.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa)
DTSTART:20210209T180000Z
DTEND:20210209T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/15
DESCRIPTION:Title: Affinization of monoidal categories\nby Alistair Sav
age (University of Ottawa) as part of Representation Theory and Mathematic
al Physics Seminar\n\n\nAbstract\nWe define the affinization of an arbitra
ry monoidal category\, corresponding to the category of string diagrams on
the cylinder. We also give an alternative characterization in terms of a
djoining dot generators to the category. The affinization formalizes and
unifies many constructions appearing in the literature. We describe a lar
ge number of examples coming from Hecke-type algebras\, braids\, tangles\,
and knot invariants.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Sheinman (Steklov Mathematical Institute\, Moscow)
DTSTART:20210216T180000Z
DTEND:20210216T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/16
DESCRIPTION:Title: Lax representation and separation of variables for Hitch
in systems\nby Oleg Sheinman (Steklov Mathematical Institute\, Moscow
) as part of Representation Theory and Mathematical Physics Seminar\n\n\nA
bstract\nThe Hitchin systems were invented in 1987 and since that time hav
e been\nsuccessfully applied in geometric Langlands program\, Supersymmet
ric\nModels of quantum field theory (SUSY)\, 2D CFT and in other fields.
In\n1987-97 Hitchin systems have been investigated mainly by methods of\na
lgebraic geometry but later it was realized that they also need to be\ninv
estigated by specific methods of the theory of integrable systems\n(K.Gawe
dzki’98\, R.Donagi\, E.Witten’95\, A.Gorsky\, N.Nekrasov\,\nV.Rubtsov
’01\, I.Krichever’01). In my talk\, I will report on some\nexplicit re
sults in this direction. To begin with\, I shall define\nHitchin systems b
y means of the Lax representation with spectral\nparameter on a Riemann su
rface. For Lax operators taking values in gl(n)\nit is due to I.Krichever
(2001). Based on the description of gradings of\ncomplex semi-simple Lie a
lgebras\, I shall give the definition in the\ncase of an arbitrary Lie alg
ebra of that class (mainly focusing on the\nsimple case). Then I’ll des
cribe the universal spectral curve for\nHitchin systems on hyperelliptic c
urves. It makes possible to apply the\nclassical method of separation of v
ariables. Following this line\, I’ll\ngive completely explicit (at least
for Lie algebras An\, Bn\, Cn\, and\nhyperelliptic curves) expressions fo
r the Hamiltonians and angle\nvariables of Hitchin systems.\n\n
References\nO. K. Sheinman. Lax operator algebras and integrable s
ystems. Russian\nMath. Surveys\, 71:1 (2016)\, 109–156\; arXiv:1602.0432
0.\n\nO.K.Sheinman. Spectral curves of the hyperelliptic Hitchin systems.\
nFunct. Anal. Appl.\, 53:4 (2019)\, 291–303\; arXiv:1806.10178.\n\nP.I.B
orisova\, O.K.Sheinman. Hitchin systems on hyperelliptic curves.\nProceedi
ngs of the Steklov Mathematical Institute\, Vol. 311\, 2020\;\narXiv:1912.
06849.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harnad (Concordia University\, Mathematical Physics Lab\, Cen
tre de recherches mathématiques)
DTSTART:20210223T180000Z
DTEND:20210223T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/17
DESCRIPTION:Title: Bilinear expansions of lattices of KP $\\tau$-function
in BKP $\\tau$-functions: a fermionic approach\nby John Harnad (Concor
dia University\, Mathematical Physics Lab\, Centre de recherches mathémat
iques) as part of Representation Theory and Mathematical Physics Seminar\n
\n\nAbstract\nThe notion of Kadomtsev-Petviashvili (KP) and BKP $\\tau$ fu
nctions will\nbe recalled\, together with their representations as fermion
ic expectation values.\nSchur-type lattices of such KP and BKP $\\tau$-fun
ctions will be defined\, corresponding to\na given infinite general linear
or orthogonal group element\, labelled by partitions\nand strict partitio
ns respectively. A bilinear expansion expressing elements of these lattice
s of KP $\\tau$-functions as sums over products of pairs of elements of as
sociated lattices of BKP $\\tau$-functions will be presented\, generalizi
ng earlier results relating determinants and Pfaffians of minors of skew
symmetric matrices\, with applications to Schur functions and Schur $Q$-fu
nctions. Further applications include inhomogeneous polynomial $\\tau$-fun
ctions of KP and BKP type\, with their determinantal and Pfaffian represen
tations.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vidas Regelskis (University of Hertfordshire)
DTSTART:20210302T180000Z
DTEND:20210302T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/18
DESCRIPTION:Title: R-matrix presentation of orthogonal and symplectic quant
um loop algebras\nby Vidas Regelskis (University of Hertfordshire) as
part of Representation Theory and Mathematical Physics Seminar\n\n\nAbstra
ct\nIn this talk I will present an R-matrix approach to quantum loop\nalge
bras associated with the simple Lie algebras of orthogonal and\nsymplectic
types. One of the main advantages of the R-matrix approach\nover the Drin
feld new presentation is that both untwisted and twisted\ncases can be con
sidered seamlessly with no extra effort. I will also\ndiscuss challenges a
nd advantages of the R-matrix approach in proving\nthe PBW theorem and con
structing highest-weight representations\, and\nrediscovering the classica
l results of Chari and Pressley.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Pevtsova (University of Washington)
DTSTART:20210420T170000Z
DTEND:20210420T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/19
DESCRIPTION:Title: Support and tensor product property for integrable finit
e dimensional Hopf algebras.\nby Julia Pevtsova (University of Washing
ton) as part of Representation Theory and Mathematical Physics Seminar\n\n
\nAbstract\nFor a finite dimensional Hopf algebra A the cohomological supp
ort on the stable category Stab A can be defined via the Benson-Iyengar-Kr
ause theory of local cohomology functors\, with no reference to the tensor
structure.\n\n Yet\, for various finite tensor categories the cohomologi
cal support turns out to respect that structure via the “tensor product
property”: $supp(M \\otimes N) = supp M \\cap supp N$. \nWhen the proper
ty holds\, it often appears to be intimately connected with some kind of a
lternative description of the cohomological support\, “a rank variety”
. I’ll describe such an alternative construction\, the hypersurface supp
ort\, which goes back to the work of Eisenbud\, Avramov\, Buchweitz and Iy
engar in commutative algebra\, in the case of a finite dimensional integra
ble Hopf algebra. Applications include (only some) small quantum groups\,
quantum linear spaces\, Drinfeld doubles of finite group schemes\, rings o
f functions on finite group schemes and elementary finite supergroup schem
es. Joint work with C. Negron and D. Benson\, S. Iyengar\, H. Krause.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Mukhin (IUPUI)
DTSTART:20210316T170000Z
DTEND:20210316T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/20
DESCRIPTION:Title: Characters\, q-characters\, and qq-characters\nby Ev
geny Mukhin (IUPUI) as part of Representation Theory and Mathematical Phys
ics Seminar\n\n\nAbstract\nThe q-characters of finite dimensional modules
of affine quantum groups describe the cancellation of poles of transfer m
atrices in analytic Bethe ansatz. The qq-characters are combinatorial obje
cts which describe the commutation of deformed W-currents with screening c
harges in a similar way.\n\nIn this talk I will try to give an elementary
introduction to the theory of q- and qq-characters\, discuss the related c
ombinatorics and outline the main ideas and challenges in the area.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oksana Yakimova (Friedrich-Schiller-Universität Jena Mathematisch
es Institut)
DTSTART:20210323T170000Z
DTEND:20210323T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/21
DESCRIPTION:Title: On the Feigin-Frenkel centre and its applications to qua
ntisation problems\nby Oksana Yakimova (Friedrich-Schiller-Universitä
t Jena Mathematisches Institut) as part of Representation Theory and Mathe
matical Physics Seminar\n\n\nAbstract\nLet $G$ be a complex reductive grou
p\, set $\\mathfrak g={\\mathrm{Lie\\\,}}G$. The symmetric algebra ${\\ma
thcal S}(\\mathfrak g)$ is equipped with the standard Lie—Poisson bracke
t and a subalgebra $A\\subset {\\mathcal S}(\\mathfrak g)$ is Poisson-comm
utative if this bracket vanishes on $A$. Since ${\\mathcal S}(\\mathfrak g
)$ is the associated graded of the enveloping algebra ${\\mathcal U}(\\mat
hfrak g)$\, it is natural to ask\, whether a given Poisson-commutative $A\
\subset {\\mathcal S}(\\mathfrak g)$ has a quantisation (a lift to a commu
tative subalgebra of ${\\mathcal U}(\\mathfrak g)$).\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hadi Salmasian (University of Ottawa)
DTSTART:20210330T170000Z
DTEND:20210330T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/22
DESCRIPTION:Title: Capelli problems for basic classical Lie superalgebras\nby Hadi Salmasian (University of Ottawa) as part of Representation The
ory and Mathematical Physics Seminar\n\n\nAbstract\nLet $g$ be a basic cla
ssical Lie superalgebra and let $V$ be a representation of $g$ such that $
S(V)$ is a multiplicity-free $g$-module. In this setting\, one can constru
ct a natural basis for the algebra of $g$-invariant (super)polynomial diff
erential operators on $V$. When the pair $(g\,V)$ arises from the Tits-Kan
tor-Koecher construction\, we compute an explicit formula for the eigenval
ues of this family of operators. We connect this formula to the deformed r
oot systems of type $A(m\,n)$ that were studied by Sergeev and Veselov. As
a byproduct\, we prove that for $(g\,V)$ associated to the exceptional 10
-dimensional Jordan superalgebra\, the abstract Capelli problem (in the se
nse of Howe and Umeda) has a negative answer. Based on joint work with S.
Sahi and V. Serganova.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Kashuba (Institute of Mathematics and Statistics University
of Sao Paulo)
DTSTART:20210427T170000Z
DTEND:20210427T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/23
DESCRIPTION:Title: Representation type of Jordan algebras and superalgebras
\nby Irina Kashuba (Institute of Mathematics and Statistics University
of Sao Paulo) as part of Representation Theory and Mathematical Physics S
eminar\n\n\nAbstract\nWe will review recent and classical results on the r
epresentations of finite dimensional Jordan algebras and superalgebras. We
will weigh the pros against the cons of using the Tits-Kantor-Koecher con
struction for this problem.\n\nThe seminar presentation is joint with S
pringfest in honor of Vera Serganova\nhttps://innaentova.wixsite.com/sprin
gfest2021\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zongzhu Lin (Kansas State University)
DTSTART:20210406T170000Z
DTEND:20210406T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/24
DESCRIPTION:Title: Irreducible characters for algebraic groups in positive
characteristics and quantum groups at $p^r$-th roots of 1.\nby Zongzhu
Lin (Kansas State University) as part of Representation Theory and Mathem
atical Physics Seminar\n\n\nAbstract\nIrreducible characters for reductive
algebraic groups in positive characteristic $p$ cases were conjectured by
Lusztig in terms of Weyl characters using Kazhdan-Lusztig polynomials whe
n the highest weight is reasonably within the $p^2$-alcove. When $p$ is su
fficiently large such that all restricted dominant weights are within this
region\, Lusztig conjectured formula would give all irreducible character
s using the Steinberg tensor product theorem. However decomposing Weyl ch
aracters in terms of irreducible characters and expressing irreducible cha
racters in terms of Weyl characters becomes much more complicated when the
highest weight is outside of $p^2$ alcove. In 2014\, Lusztig gave a recur
sive formula to computing these dcomposition numbers. In this talk\, I wil
l use the irreducible characters for quantum groups at $p^r$-th roots of u
nity as middle bridge for $r=1\, 2\, …$ to express the decomposition num
bers in terms of Kazhdan Lusztig polynomials with different affine Weyl gr
oup actions on the weight lattice through Frobenius twists. When r=1\, we
recover Lusztig’s formula. Not only we get infinite family of Z-bases fo
r the Weyl group invariants in the group ring of the weight lattices\, but
we also obtain infinite families of highest weight modules corresponding
to these bases.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thorsten Heidersdorf (Mathematical Institute of the University of
Bonn)
DTSTART:20210413T170000Z
DTEND:20210413T180000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/25
DESCRIPTION:Title: Monoidal structures for supergroups\nby Thorsten Hei
dersdorf (Mathematical Institute of the University of Bonn) as part of Rep
resentation Theory and Mathematical Physics Seminar\n\n\nAbstract\nVery li
ttle is known about the rules governing the tensor product decomposition b
etween irreducible representations of an algebraic supergroup. It turns ou
t that one can understand the decomposition "up to superdimension 0". For
$GL(m|n)$ ($m \\geq n$) this can in some way be reduced to the case $GL(m|
2)$\, so I will mostly discuss this case along with some preliminary resul
ts for $OSp(m|2n)$.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khoa Nguyen (University of Texas\, Arlington)
DTSTART:20210309T180000Z
DTEND:20210309T190000Z
DTSTAMP:20260404T110643Z
UID:RepTheoryMathPhys/26
DESCRIPTION:Title: Exponentiation functors on differential operators of $\\
mathfrak{sl}(n+1)$.\nby Khoa Nguyen (University of Texas\, Arlington)
as part of Representation Theory and Mathematical Physics Seminar\n\n\nAbs
tract\nWith the aid of the exponentiation functor and Fourier transform we
introduce modules $T (g\, V\, S)$ of differential operators of $\\mathf
rak{sl}(n + 1)$. Here $g$ is a polynomial of n variables\, $V$ is a $\\mat
hfrak{gl}(n)$-module\, and $S$ is a subset of $\\{1\,2\,…\,n\\}$. By var
ying $g\,V\,S$ we obtain various families of modules of $\\mathfrak{sl}(n
+ 1)$. Some of these families contain weight modules (i.e. with a semisiml
e action of the Cartan subalgebra $\\mathfrak h$)\, while others contain $
\\mathfrak h$-free modules. An isomorphism theorem and simplicity criterio
n for $T (g\, V\, S)$ will be provided. This is based on a joint work with
D. Grantcharov.\n
LOCATION:https://stable.researchseminars.org/talk/RepTheoryMathPhys/26/
END:VEVENT
END:VCALENDAR